### New Publications O ered by the AMS

Discrete Mathematics and Combinatorics

# General and Interdisciplinary

## Niels Henrik Abel

Combinatorial Geometry and Its Algorithmic Applications

## The Alcalá Lectures

János Pach, Courant Institute of Mathematical Sciences, New York, NY, and Micha Sharir, Tel Aviv University, Israel

Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks.

Combinatorial Geometry and Its Algorithmic Applications is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography.

This item will also be of interest to those working in applications.

Contents: Sylvester-Gallai problem: The beginnings of combinatorial geometry; Arrangements of surfaces: Evolution of the basic theory; Davenport-Schinzel sequences: The inverse Ackermann function in geometry; Incidences and their relatives: From Szemerédi and Trotter to cutting lenses; Crossing numbers of graphs: Graph drawing and its applications; Extremal combinatorics: Repeated patterns and pattern recognition; Lines in space: From ray shooting to geometric transversals; Geometric coloring problems: Sphere packings and frequency allocation; From Sam Loyd and László Fejes Tóth: The 15 puzzle and motion planning; Bibliography; Index.

Mathematical Surveys and Monographs, Volume 152

January 2009, 235 pages, Hardcover, ISBN: 978-0-8218-4691-9, LC 2008038876, 2000 Mathematics Subject Classification: 05C35, 05C62, 52C10, 52C30, 52C35, 52C45, 68Q25, 68R05, 68W05, 68W20, AMS members US$60, List US$75, Order code SURV/152

Mathematician Extraordinary

### Øystein Ore

This is a story of more than a century ago, about a circle of young scientists, and in particular one among them, a mathematician, Niels Henrik Abel. He is well known to any mathematician of today; indeed, few men have their name associated with so many results and concepts in modern mathematics. This, however, is not the main concern in this book. It is rather the simple story of a scientist, his family and friends, his hopes and sorrows, his triumphs and tragedies. Many great lives, rich in outer events, have inspired biographers. But the profound humanity of a searching soul may provide the background for an equally arresting chronicle—the heart-warming tale of a young man who set out from a little Norwegian town to explore the world of science.

Contents: Family and childhood; At the university; Journey to the continent; The return; Epilogue; Bibliography; Index of names.

AMS Chelsea Publishing, Volume 274

October 2008, 277 pages, Hardcover, ISBN: 978-0-8218-4644-5, LC 73-14693, 2000 Mathematics Subject Classification: 01A70, 01A55, AMS members US$44, List US$49, Order code CHEL/274.H

# Geometry and Topology

## Singularities II

Geometric and Topological Aspects

Jean-Paul Brasselet, Institut de Mathématiques de Luminy-CNRS, Marseille, France, José Luis Cisneros-Molina, Universidad Nacional Autónoma de México, Cuernavaca, Mexico, David Massey, Northeastern University, Boston, MA, José Seade, Universidad Nacional Autónoma de México, Cuernavaca, Mexico, and Bernard Teissier, Institut Mathématique de Jussieu-CNRS, Paris, France, Editors

This is the second part of the proceedings of the “School and Workshop on the Geometry and Topology of Singularities”, held in Cuernavaca, Mexico, from January 8 to 26 of 2007, in celebration of the 60th Birthday of Lê Du˜ng Tráng.

This volume contains fourteen cutting-edge research articles on geometric and topological aspects of singularities of spaces and

### January 2009

Notices of the AMS

77